mechatronics

Question 1

causal system

Answer 1

a system is causal if the output at time t does not depend on the values of the input at any time t’>t

Question 2

memoryless system

Answer 2

a causal system is memoryless if the output at time t depends only on the input at time t. otherwise the system has memory

Question 3

when is a system LINEAR

Answer 3

a system is linear when it is additive and homogenous

Question 4

additive:

Answer 4

if adding the inputs results in the addition of individual outputs, the system is additive
x1(t)+x2(t) -> y1(t)+y2(t)

eg. y(t) = 2x(t)
x1(t) -> 2x1(t) = y1(t)
x2(t) -> 2x2(t) = y2(t)
x1(t)+x2(t) -> 2* (x1(t)+x2(t))

Question 5

homogeneous:

Answer 5

scaling by a factor of c

Question 6

what is the complementary function

Answer 6

the solution of the damped, free vibration equation. this tells us the transient motion that dies away as steady state vibration is achieved

Question 7

what is the particular integral

Answer 7

tells us the steady state vibration at excitation frequency
this can be found by assuming a solution in the form: x = Xsin(omega*t-phi)
X-> vibration amplitude
phi-> phase angle
omega-> excitation frequency

Question 8

rotating mass unbalance force equation:

Answer 8

F=mew^2 sin(wt)

Question 9

amplitude=

Answer 9

mew^2

Question 10

torsional system eq of motion

Answer 10

I theta: + c theta. + k theta = 0

Question 11

damping frequency

Answer 11

wd = wn (1-damping coeff^2)